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Fisher-Rao geometry of Dirichlet distributions

Authors
  • Brigant, Alice Le
  • Preston, Stephen
  • Puechmorel, Stéphane
Type
Published Article
Publication Date
Nov 19, 2020
Submission Date
May 12, 2020
Identifiers
DOI: 10.1016/j.difgeo.2020.101702
Source
arXiv
License
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External links

Abstract

In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has everywhere negative sectional curvature. An important consequence of this negative curvature for applications is that the Fr{\'e}chet mean of a set of Dirichlet distributions is uniquely defined in this geometry.

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